Cellulose nanocrystals (CNCs), a ubiquitous nano-sized natural biopolymer, have drawn considerable attention in recent years due to their excellent mechanical and chemical properties. However, thermal properties of CNCs, which are critical for their potential applications as structural or functional materials, are less investigated. In this work, their thermal properties were systematically studied by molecular dynamics (MD) simulations in terms of the effects of polymorphs, size, temperature, and strain. It was found that the thermal conductivities depend on the polymorphs of CNCs, but the thermal conductance of unit chain of each polymorph is similar. Moreover, the strong dependence of the thermal conductivities of CNCs on their length and cross-sectional area indicates the existence of remarkable ballistic-diffusive phonon transport. Single chain CNCs can achieve a thermal conductivity of similar to 6 W/(m.K), implying their potential as high thermal conductive polymer. The mechanical strain can enhance the alignment of cellulose skeleton, which reduces phonon scattering and thus increases thermal conductivity. Possible underlying mechanism of the varying thermal conductivity was further discussed and attributed to the shift of phonon frequencies and varied degree of orientation. This study reveals the sophisticated ballistic-diffusive phonon transport in CNCs, and pave path to future design of CNC-based materials with desirable thermal properties. (C) 2019 Elsevier Ltd. All rights reserved